Signals & Systems I: Fourier Transformation and Distributions

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Related lectures (30)

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Fourier Transformation: Fundamentals

Covers the fundamentals of the Fourier transformation, including decreasing causal exponential signals and the Schwartz class.

Fourier Transform of Tempered Distributions: Reflection and Translation

Explores the Fourier transform of tempered distributions, emphasizing reflection and translation operations.

Signal Representations

Covers matrix operations, Fourier transformations, Gaussian models, and signal representations using algebraic methods.

Fundamental Solutions of Laplace Equation

Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

Distributions & Interpolation Spaces

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Fourier Transform: Concepts and Applications

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.

Distribution & Interpolation Spaces

Covers the concept of distributions with compact support and their interpolation spaces.

Compression

Covers the concept of compression and constructing prefix-free codes based on given information.

Generalization Error

Discusses mutual information, data processing inequality, and properties related to leakage in discrete systems.

Compression: Prediction

Covers the concepts of compression and prediction using prefix-free codes and distributions.

Probability and Statistics

Covers probability distributions, moments, and continuous random variables.

Signals & Systems I: Distributions and Linear Systems

Covers distributions, linear systems, impulse response, convolution, and examples of linear systems.

Probability Theory: Random Variables and Distributions

Introduces probability theory, random variables, and distributions, with a focus on their applications in atomic diffusion.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Introduction to Distributions

Covers Green's representation formula, fundamental solutions, and distribution properties.

Distributions and Laplace Transform: Key Concepts

Discusses distributions, the Laplace transform, and their applications in mathematical analysis.

Cut-off Phenomenon: Proof Ideas

Explores proof ideas related to the cut-off phenomenon and its implications in random walks on hypercubes.

Elements of Statistics: Estimation & Distributions

Covers fundamental statistics concepts, including estimation theory, distributions, and the law of large numbers, with practical examples.

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